A breathing system with a circulation of breathing air is known from U.S. Pat. No. 6,805,119 B2. The known breathing system has a layered structure and includes a breathing gas block, a valve plate and a cover. The breathing gas block is provided with breathing gas connections via which the patient is supplied with breathing gas. Partition walls are located within the breathing gas block through which breathing gas channels are formed within the breathing gas block. The valve plate has directional valves which are located on the upper side of the valve plate and with which the direction of the breathing gas flow can be controlled. The cover is located above the valve plate. The cover forms the upper end of the breathing system and is connected to the breathing gas block via a quick acting closure system. In components which are fixed on the metallic valve plate, it is important that, on the one hand, easy cleaning is possible at the connection joints and that components can be exchanged without the use of tools by the service. On the other hand, the fixation of the components must be so stable that the connection joints cannot be accidentally disengaged.